{"id":"https://openalex.org/W3043678174","doi":"https://doi.org/10.3390/a13070170","title":"On the Well-Posedness of A High Order Convective Cahn-Hilliard Type Equations","display_name":"On the Well-Posedness of A High Order Convective Cahn-Hilliard Type Equations","publication_year":2020,"publication_date":"2020-07-16","ids":{"openalex":"https://openalex.org/W3043678174","doi":"https://doi.org/10.3390/a13070170","mag":"3043678174"},"language":"en","primary_location":{"id":"doi:10.3390/a13070170","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13070170","pdf_url":"https://www.mdpi.com/1999-4893/13/7/170/pdf?version=1594882912","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/13/7/170/pdf?version=1594882912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052902271","display_name":"Giuseppe Maria Coclite","orcid":"https://orcid.org/0000-0001-6019-4757"},"institutions":[{"id":"https://openalex.org/I68618741","display_name":"Polytechnic University of Bari","ror":"https://ror.org/03c44v465","country_code":"IT","type":"education","lineage":["https://openalex.org/I68618741"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Giuseppe Maria Coclite","raw_affiliation_strings":["Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy","institution_ids":["https://openalex.org/I68618741"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038198270","display_name":"Lorenzo di Ruvo","orcid":"https://orcid.org/0000-0002-4179-7867"},"institutions":[{"id":"https://openalex.org/I5561750","display_name":"University of Bari Aldo Moro","ror":"https://ror.org/027ynra39","country_code":"IT","type":"education","lineage":["https://openalex.org/I5561750"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lorenzo di Ruvo","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Bari, 70125 Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Bari, 70125 Bari, Italy","institution_ids":["https://openalex.org/I5561750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052902271"],"corresponding_institution_ids":["https://openalex.org/I68618741"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8797,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.69696742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"13","issue":"7","first_page":"170","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9381999969482422,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.8995208740234375},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.5446758270263672},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5370774269104004},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.5168417096138},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4905194640159607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4643920063972473},{"id":"https://openalex.org/keywords/pulmonary-surfactant","display_name":"Pulmonary surfactant","score":0.4378364086151123},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3324722945690155},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28429222106933594},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.24563312530517578},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.13645896315574646},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.1237402856349945},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09790074825286865}],"concepts":[{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.8995208740234375},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.5446758270263672},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5370774269104004},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.5168417096138},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4905194640159607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4643920063972473},{"id":"https://openalex.org/C58226133","wikidata":"https://www.wikidata.org/wiki/Q1324199","display_name":"Pulmonary surfactant","level":2,"score":0.4378364086151123},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3324722945690155},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28429222106933594},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.24563312530517578},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.13645896315574646},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.1237402856349945},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09790074825286865},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a13070170","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13070170","pdf_url":"https://www.mdpi.com/1999-4893/13/7/170/pdf?version=1594882912","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1801fa5736a54c3db263d1b2c83ba9be","is_oa":true,"landing_page_url":"https://doaj.org/article/1801fa5736a54c3db263d1b2c83ba9be","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 13, Iss 7, p 170 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/13/7/170/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a13070170","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 13; Issue 7; Pages: 170","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a13070170","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a13070170","pdf_url":"https://www.mdpi.com/1999-4893/13/7/170/pdf?version=1594882912","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3043678174.pdf","grobid_xml":"https://content.openalex.org/works/W3043678174.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W100484353","https://openalex.org/W956831182","https://openalex.org/W1869546340","https://openalex.org/W1964896841","https://openalex.org/W1977255739","https://openalex.org/W1978081787","https://openalex.org/W1979546093","https://openalex.org/W1982999858","https://openalex.org/W1986972441","https://openalex.org/W1994466207","https://openalex.org/W2013257838","https://openalex.org/W2022019833","https://openalex.org/W2028821645","https://openalex.org/W2029104307","https://openalex.org/W2029792495","https://openalex.org/W2032270660","https://openalex.org/W2034024496","https://openalex.org/W2034390751","https://openalex.org/W2037933894","https://openalex.org/W2043383000","https://openalex.org/W2049967935","https://openalex.org/W2057606844","https://openalex.org/W2057808716","https://openalex.org/W2059691352","https://openalex.org/W2062713613","https://openalex.org/W2072655083","https://openalex.org/W2073061323","https://openalex.org/W2079610671","https://openalex.org/W2080044677","https://openalex.org/W2085062755","https://openalex.org/W2094925628","https://openalex.org/W2098722835","https://openalex.org/W2107634631","https://openalex.org/W2114029156","https://openalex.org/W2115171184","https://openalex.org/W2124232799","https://openalex.org/W2131868609","https://openalex.org/W2139886236","https://openalex.org/W2154839486","https://openalex.org/W2155430897","https://openalex.org/W2164471548","https://openalex.org/W2169920821","https://openalex.org/W2170544117","https://openalex.org/W2174967758","https://openalex.org/W2184633288","https://openalex.org/W2211627007","https://openalex.org/W2222034324","https://openalex.org/W2260570520","https://openalex.org/W2317462844","https://openalex.org/W2322840440","https://openalex.org/W2802963327","https://openalex.org/W2963231808","https://openalex.org/W2963797441","https://openalex.org/W2963889733","https://openalex.org/W2964088097","https://openalex.org/W2964309749","https://openalex.org/W2970770034","https://openalex.org/W2981852112","https://openalex.org/W3001778069","https://openalex.org/W3013454424","https://openalex.org/W3014404461","https://openalex.org/W3015895242","https://openalex.org/W3100925978","https://openalex.org/W3103141722","https://openalex.org/W3142372934","https://openalex.org/W4236965075","https://openalex.org/W4245698330","https://openalex.org/W6639095864","https://openalex.org/W6675080516","https://openalex.org/W6686610792","https://openalex.org/W6688407262","https://openalex.org/W6688585410","https://openalex.org/W6692773433"],"related_works":["https://openalex.org/W2371901143","https://openalex.org/W2010867980","https://openalex.org/W1985596875","https://openalex.org/W1977329809","https://openalex.org/W1570392672","https://openalex.org/W2154432709","https://openalex.org/W2142360195","https://openalex.org/W1787176442","https://openalex.org/W2312327980","https://openalex.org/W2974249720"],"abstract_inverted_index":{"High":[0],"order":[1],"convective":[2],"Cahn-Hilliard":[3],"type":[4],"equations":[5],"describe":[6],"the":[7,14,28,31,35],"faceting":[8],"of":[9,16,30],"a":[10],"growing":[11],"surface,":[12],"or":[13],"dynamics":[15],"phase":[17],"transitions":[18],"in":[19],"ternary":[20],"oil-water-surfactant":[21],"systems.":[22],"In":[23],"this":[24,40],"paper,":[25],"we":[26],"prove":[27],"well-posedness":[29],"classical":[32],"solutions":[33],"for":[34],"Cauchy":[36],"problem,":[37],"associated":[38],"with":[39],"equation.":[41]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}